Solvability of a free-boundary problem for a heterogeneous elastic body

We consider the free-boundary problem for a stationary elastic system. We prove that the problem has a classical solution if the initial data are close to the stationary solution.     

Rectifying diodes from asymmetrically functionalized single-wall carbon nanotubes

Asymmetrically functionalized single-wall carbon nanotubes (SWNTs) have been prepared by a covalent reaction of an 11-mercaptoundecanol-modified Au surface with oxidized SWNT cylinders. While one end of the tubes is attached to gold substrate via ester groups, the free carboxylic substituents on the other end can be either ionized (CO2-) or esterified (CO2Et), creating a donor-acceptor asymmetric and acceptor-acceptor symmetric SWNT, respectively. Study of the SWNT monolayer conductance in Hg drop junction experiments reveals a pronounced diode-like behavior for donor-SWNT-acceptor junctions, while acceptor-SWNT-acceptor junctions are electrically symmetric.     

Lie symmetries and form-preserving transformations of reaction-diffusion-convection equations

New Lie symmetry classification of the known class of reaction-diffusion-convection equations is presented. The classification method is based on combining the standard group classification method and the form-preserving transformation approach.     

S掺杂纳米多孔碳的光催化活性:表面化学和孔隙率的重要性(英文)

This minireview summarizes our recent findings on the photoactivity of S-doped nanoporous carbons. The materials were either synthesized from the sulfur-containing polymers or obtained by heat treatment of commercial carbon with hydrogen sulfide. Their surface was extensively charac terized from the points of view of its surface chemistry, porosity, morphology, and electronic properties. The carbons showed enhanced activity towards oxidation of arsine and removal of diben-zothiophenes from model diesel fuel. The latter were oxidized to various oxygen containing intermediates and the cleavage of C–C bonds in aromatic ring was detected when carbon with adsorbed species was exposed to UV or visible light. Irradiation resulted in generation of photocurrent in a broad range of wavelength. The presence of sulfur led to the reduction of oxygen and contributed to an increased capacitive performance. We link these effects to the presence of reduced sulfur in the small pores which enhances the dispersive interactions via inducing a positive charge to carbon atoms, to sulfur in oxygenated forms which contribute to Faradaic reactions and increase the polar interactions, and to the hydrophobicity of a surface in small pores where oxygen can be reduced by excited electrons from chromophoric-like sulfur containing groups.     

Pyrrolidylsubstituted Azadipyrromethene with Fully Chelated Boron Atom

A difluorosubstituted aza-boron–dipyrromethene derivative with fully chelated boron atom was synthesized by the reaction of BF₃ · Et₂O with 3,3,5,5-tetraarylazadipyrromethene, which was easily prepared from 1,3-diaryl-4-nitro-butan-1-one and ammonium acetate. One fluorine atom of the dye was substituted by pyrrolidine residue. This resulted in a significant bathochromic effect. Ultraviolet absorption and fluorescence emission spectra were recorded, and quantum yields of the obtained compounds were calculated.     

Synthesis of 1-(R-Phenyl)-5-(R-Methyl)-1H-1,2,3-triazole-4-carboxylic Acids by One-Pot Tandem Reaction

Substituted 1H-1,2,3-triazole-4-carboxylic acids were synthesized by a three-component reaction of arylazides, ethyl 4-chloro-3-oxobutanoate, and either O- or S-nucleophiles in the presence of a base catalyst. The reaction most probably proceeded as a [3 + 2] cyclocondensation reaction between arylazide and ethyl 4-chloro-3-oxobutanoate with the further nucleophilic substitution of chlorine in the chloromethyl group. Reaction optimization was performed to carry out the reaction with an O-nucleophile. Conditions were found under which diethyl 2,5-dihydroxyterephthalate (the product of self-condensation of two molecules of ethyl 4-chloro-3-oxobutanoate with the further oxidation by azide) was obtained.     

Topological and fractal properties of real numbers which are not normal

The set L of essentially non-normal numbers of the unit interval (i.e., the set of real numbers having no asymptotic frequencies of all digits in their nonterminating s-adic expansion) is studied in details. It is proven that the set L is generic in the topological sense (it is of the second Baire category) as well as in the sense of fractal geometry (L is a superfractal set, i.e., the Hausdorff-Besicovitch dimension of the set L is equal 1). These results are substantial generalizations of the previous results of the two latter authors [M. Pratsiovytyi, G. Torbin, Ukrainian Math. J. 47 (7) (1995) 971-975].The Q^∗-representation of real numbers (which is a generalization of the s-adic expansion) is also studied. This representation is determined by the stochastic matrix Q^∗. We prove the existence of such a Q^∗-representation that almost all (in the sense of Lebesgue measure) real numbers have no asymptotic frequency of all digits. In the case where the matrix Q^∗ has additional asymptotic properties, the Hausdorff-Besicovitch dimension of the set of numbers with prescribed asymptotic properties of their digits is determined (this is a generalization of the Eggleston-Besicovitch theorem). The connections between the notions of “normality of numbers” respectively of “asymptotic frequencies” of their digits is also studied.     

A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity

This paper presents the development of a physical-based constitutive model for the representation of viscous effects in rubber-like materials. The proposed model originates from micromechanically motivated diffusion processes of the highly mobile polymer chains described within the formalism of Brownian motion. Following the basic assumption of accounting for the elastic and the viscous effects in rubber viscoelasticity by their representation through a separate elastic ground network and several viscous subnetworks, respectively, the kinetic theory of rubber elasticity is followed and extended to represent also the viscous contribution in this work. It is assumed that the stretch probability of certain chain segments within an individual viscous subnetwork evolves based on the movement of the chain endpoints described by the Smoluchowski equation extended in this work from non-interacting point particles in a viscous surrounding to flexible polymer chains. An equivalent tensorial representation for this evolution is chosen which allows for the closed form solution of the macroscopic free energy and the macroscopic viscous overstress based on a homogenization over the probability space of the introduced micro-objects. The resulting model of the viscous subnetwork is subsequently combined with the non-affine micro-sphere model and applied in homogeneous and non-homogeneous tests. Finally, the model capacity is outlined based on a comparison with in the literature available experimental data sets.     

Morphological and chemical features of nano and macroscale carbons affecting hydrogen peroxide decomposition in aqueous media

Stable film-forming nanocomposite particles with diameters ranging from 120 to 300 nm, based on polybutylmethacrylate (PBMA) and cellulose whiskers in water dispersions, were successfully synthesized in one step through mini-emulsion polymerization. The nanocomposite dispersion with a solid content of 25 wt.% and up to 5 wt.% of nanofiller loading was prepared by in situ polymerization, in the presence of the whiskers using dodecylpyridinium chloride (DPC), as a cationic surfactant, and 2,2-azobis(isobutyronitrile) (AIBN), as initiator. The electrostatic interaction between the positively charged droplets and negatively charged whiskers ensured the anchoring of the nanofiller around the polymer particles. The ensuing dispersions were characterized by Dynamic Light Scattering (DLS), ζ-Potential Measurements, and Field-Emission Scanning Electron Microscopy (FE-SEM). After the film formation process, the nanocomposite film exhibits a high transparency, denoting the good dispersion of the whiskers throughout the matrix.